Input: height = [1,8,6,2,5,4,8,3,7]
Explanation: The above vertical lines are represented by array [1,8,6,2,5,4,8,3,7]. In this case, the max area of water (blue section) the container can contain is 49.
Input: height = [1,1]
1. Understanding the Problem:
The problem statement requires us to find the two lines on a 2D plane that form a container with the most water. The input is an array of non-negative integers, where each integer represents the height of a vertical line at a particular index. Our task is to determine the maximum amount of water that can be trapped by the container formed by any two lines from the array.
To solve this problem efficiently, we can use the two-pointer technique. We’ll start with two pointers, one at the beginning of the array and the other at the end. We’ll calculate the area between the lines represented by these two pointers and keep track of the maximum area found so far. Then, we’ll move the pointer with the smaller height inward, as moving the pointer with the larger height wouldn’t yield a larger area.
4. Time and Space Complexity:
The two-pointer approach reduces the time complexity to O(n), where n is the number of elements in the height array, as we iterate through the array only once. The space complexity is O(1) since we use a constant amount of extra space.